CN106771662A - A kind of method based on the remote Electromagnetic Calculation of simplification - Google Patents

Abstract

The present invention relates to lighting location technology and Electromagnetic Calculation field, it is characterized in that：Calculate first and propagate electric field and the magnetic field of certain distance under ideal conditions (radius of curvature of the earth infinitely great, electrical conductivity infinitely great), and carry out Fourier transform and obtain frequency domain；Electrical conductivity decay factor W is calculated respectively₁With radius of curvature of the earth decay factor W₂, two factors and ideal field are carried out into convolution, obtain electric field and the magnetic field of frequency domain decay；Carry out inverse fourier transform and obtain final product time domain decay electric field and magnetic field.Contrast amendment can be carried out to result of calculation using Finite-Difference Time-Domain Method (FDTD), make result of calculation more accurate credible, it is more convenient to calculate the purpose that remote electromagnetic field is propagated so as to reach simplified Wait algorithms.

Description

A kind of method based on the remote Electromagnetic Calculation of simplification

Technical field

The present invention relates to lighting location and Electromagnetic Calculation field, specifically refer to that one kind calculates decay using Matlab language The factor, the method that convolution tries to achieve decay electromagnetic field is carried out with ideal field.

Background technology

The very low frequency (VLF, 3-30kHz) and low frequency (LF, 30-300kHz) signal that thunder and lightning is produced can propagate far, Several hundred kilometers can be observed to thousands of kms.Earthwave is propagated along earth surface, is mainly received in communication process , there is decay and dispersion in the influence of earth's surface electrical conductivity.Simultaneously because propagation distance is remote, the influence that earth curvature is caused is considered, Observed result can be made to propagate different compared to along straight direction.These factors of influence meeting disturbance-observer person judges according to observation data Lightning types, inverting current moment, carry out ground lightning location etc..

The electromagnetic field that thunder and lightning is produced includes horizontal component of electric field, vertical electric field and the part of horizontal magnetic field three in communication process. Delfino^[1],[2]The validity of Cooray-Rubinstein (C-R) algorithm is have studied, this algorithm is used for calculating thunder and lightning generation Horizontal component of electric field, Delfino points out that C-R algorithms have a preferable computational accuracy.Horizontal component of electric field includes a large amount of radio-frequency components, is passing Broadcast apart from it is far when almost all attenuate, remote observation mainly gathers vertical electric field signal and horizontal magnetic field signal.For The research of vertical electric field, Cooray^[3],[4]The degree of accuracy of approximate data is demonstrated Deng the accurate solution integrated using Sommerfeld. Shooray^[5]The accuracy of Wait algorithms is have studied Deng using Finite-Difference Time-Domain Method (FDTD), and is pointed out logical apart from lightning In the range of road 10-100km, the vertical electric field peak value that Wait algorithms are calculated has right well with waveform and the result of calculation of FDTD Should.When signal propagation distance reaches thousands of miles, the VLF waveguide propagation modes type of long wavelength is by success development and application, this mould Type is more suitable for the beacon signal of narrow frequency range.For the broadband signal that natural lightning is produced, this model has been filtered excessively Wave character, causes result different from the signal for fighting back generation, makes the signal for receiving more like a pulse signal rather than sudden strain of a muscle Electric signal.Cummer^[6]And Hu^[7]Propose a kind of improved two-dimentional cylindrical coordinates FDTD models, this model can be used to calculate ground- Ionosphere electromagnetic field is propagated, and cut-off frequency is 30kHz.The result of this algorithm and Pappert and Feguson^[8]Waveguide modes There is good uniformity, the lightning observed result with ELF-VLF is corresponding.But compared to Wait algorithms, this model calculates the time It is more long and restricted to calculating frequency, there is chromatic dispersion problem in calculating process.

The electromagnetic field signal produced present invention is primarily concerned with lightning propagates to the spy of distant location (hundreds of to thousands of kilometers) Levy, these signals play vital effect for the inverting of global lightning location, current moment and electric charge square.Although Wait is calculated Method^{[9],[10],[11]}The computational methods that remote electromagnetic field is propagated are already indicated above, but this algorithm is excessively complicated in calculating process, this Invention attempts to a kind of approximate data and the propagation of remote electromagnetic field is calculated, to simplify calculating process.

Technical solution step of the invention is as follows：

Step 1, calculates propagation certain distance (number under ideal conditions (radius of curvature of the earth is infinitely great, and electrical conductivity is infinitely great) Hundred kms) electric field E₀With magnetic field B₀, carry out Fourier transform and obtain frequency domain E_wAnd B_w；

E_w=fft (E₀), B_w=fft (1)

Step 2, according to W.Sollfery^[12]The approximate data of proposition, calculates Curvature decay factor W₁：

Ts is represented by：

t_s=e^-iπ/3τ_s=e^-iπ/3(3πv_s/2)^2/3

Step 3, according to Wait algorithms, calculates electrical conductivity decay factor W₂：

Δ is soil Equivalent Surface impedance, and expression formula is

Step 4, the decay factor W that will be calculated₁、W₂Respectively with ideal frequency domain E_w、B_wCarry out convolution and obtain frequency domain declining Subtract an E_G、B_G, carry out the decay electric field E that inverse fourier transform obtains final product time domain_tWith magnetic field B_t。

E_G=E_w×W₁×W₂, B_G=B_w×W₁×W₂ (7)

E_t=ifft (E_G), B_t=ifft (B_G) (8)

It is an advantage of the invention that：

1. compared to traditional Wait algorithms, approximate data proposed by the present invention simplifies calculating process, while can protect again Card result of calculation accuracy within the specific limits, for the decay that remote electromagnetic field is propagated provides new calculating thinking.

Compared to Finite-Difference Time-Domain Method (FDTD), the calculating time can be saved using this algorithm, while two methods are obtained The result for arriving is close, optimizes traditional Wait algorithms.

Brief description of the drawings

Fig. 1 method overview flow charts based on the remote Electromagnetic Calculation of simplification of the invention；

Fig. 2-1 is preferable electric field wave shape figure at 300km；

Fig. 2-2 is preferable field waveform figure at 300km；

Fig. 3-1 is the electric field oscillogram that decays at 300km；

Fig. 3-2 is decaying magnetic field oscillogram at 300km.

Specific embodiment

The present invention is the method based on the remote Electromagnetic Calculation of simplification.It is characterized in that：Ideal conditions (is calculated first Ball radius of curvature is infinitely great, and electrical conductivity is infinitely great) under propagate electric field and the magnetic field of certain distance, and carry out Fourier transform and obtain Frequency domain；Electrical conductivity decay factor W is calculated respectively₁With radius of curvature of the earth decay factor W₂, two factors and ideal field are rolled up Product, obtains electric field and the magnetic field of frequency domain decay；Carry out inverse fourier transform and obtain final product time domain decay electric field and magnetic field.Due to The Finite-Difference Time-Domain Method (FDTD) that Cummer is proposed has in its paper and expounds proofs adequately, and this patent is using this side Method carries out contrast amendment to result of calculation, makes result more accurate credible, so as to reach simplified Wait algorithms, more convenient calculating The purpose that remote electromagnetic field is propagated.Flow chart is as shown in Figure 1.

(1) ideal electric field and magnetic field are calculated first, and lightning source uses current moment source, and this current moment is easy to be added to FDTD Calculated in model, expression formula is

I in formula₀=20kA, ν₀=8 × 10⁷M/s, γ=3 × 10⁴/ s, a=2 × 10⁴/ s, b=2 × 10⁵/s。

Ideal electric field and the preferable magnetic field at a certain distance from propagating to are calculated using this current moment source, Fourier change is carried out Get the ideal field E of frequency domain in return₀And B₀：

E_w=fft (E₀), B_w=fft (B₀) (2)

(2) approximate data proposed according to W.Sollfery, calculates Curvature decay factor W₁：

X=(k in formula₀R_e/2)^1/3φ, k₀It is wave number, is expressed asφ represents the radian between lightning source and receiving terminal, R_eEarth radius is represented, lightning source can be expressed as ρ=R with the spherical distance of receiving terminal_e×φr。

t_sIt is represented by：

t_s=e^-iπ/3τ_s=e^-iπ/3(3πv_s/2)^2/3

The value of s is that 0,1,2,3... wherein s=0 time errors are that 0, s=1 time errors are that 0.0024, s=2 time errors are small Bigger in 0.0012, s values, error is smaller, and 0.0005 is being respectively less than more than 2 time errors.The t obtained in equation (4)_sSubstitute into Equation (3), the W for obtaining as earth curvature decay factor W₁。

(3) according to Wait algorithms, electrical conductivity decay factor W is calculated₂：

" erfc " represents error equation in formula, and d is distance between lightning channel and observation station, and ω represents angular frequency, and c is represented The light velocity,Δ is soil Equivalent Surface impedance, and expression formula is

ω is signal angular frequency, ε_rIt is ground relative dielectric constant, ε₀It is permittivity of vacuum, μ₀It is space permeability, σ It is earth's surface electrical conductivity.

(4) the decay factor W that will be calculated₁、W₂With ideal frequency domain E_WAnd B_WCarry out convolution and obtain decay frequency domain E_G And B_G, convolution process is as follows：

E_G=E_w×W₁×W₂, B_G=B_w×W₁ (8)

(5) to frequency domain collapsing field E_GAnd B_GCarry out inverse fourier transform, you can obtain the remote collapsing field E of time domain_tWith B_t。 Inverse fourier transform process is as follows：

E_t=ifft (E_G), B_t=ifft (9)

Instantiation

See ideal electric field and field waveform figure at Fig. 1 300km：

The ideal field peak value that two methods are obtained has gap, algorithm of the invention can be modified with FDTD results, makes The ideal electric field that two methods are calculated is close, so as to attenuation results analysis below.

After using identical ideal field, decay electric field and decaying magnetic field that next we will be calculated to two kinds of algorithms It is analyzed.Fig. 2 is decay at 300km electric field and field waveform figure；

As can be seen that the result that obtains of two methods is very close, illustrate can using the new algorithm of this patent proposition for contrast Accurately to calculate the decay of remote electromagnetic field.

Claims (1)

1. a kind of method based on the remote Electromagnetic Calculation of simplification, it is characterised in that comprise the following steps：

Step 1, calculates propagation certain distance (hundreds of thousand under ideal conditions (radius of curvature of the earth is infinitely great, and electrical conductivity is infinitely great) Rice) electric field E₀With magnetic field B₀, carry out Fourier transform and obtain frequency domain E_wAnd B_w；

E_w=fft (E₀), B_w=fft (1)

Step 2, according to the approximate data that W.Sollfery is proposed, calculates Curvature decay factor W₁：

$W_1=2e^{-j\mathrm{\π}/4}\sqrt{\mathrm{\π}x}{{\mathrm{\Σ}}_{s=1}^{\mathrm{\∞}}}^{!}---\left(2\right)$

Ts is represented by：

t_s=e^-iπ/3τ_s=e^-iπ/3(3πv_s/2)^2/3

$v_s=s+\frac{1}{4}-\frac{0.00795}{s+1/4}---\left(3\right)$

Step 3, according to Wait algorithms, calculates electrical conductivity decay factor W₂：

$W_2(0,d,j\mathrm{\ω})=1-j\sqrt{\mathrm{\π}p}\exp (-p)erfc(---\left(4\right)$

$p=-\frac{j\mathrm{\ω}d}{2c}{\mathrm{\Δ}}^2---\left(5\right)$

Δ is soil Equivalent Surface impedance, and expression formula is

$\mathrm{\Δ}=\frac{{({\mathrm{j\ω\ϵ}}_0\[\mathrm{\σ}+{\mathrm{j\ω\ϵ}}_0({\mathrm{\ϵ}}_r-1)\])}^{1/2}}{\mathrm{\σ}+{\mathrm{j\ω\ϵ}}_0{\mathrm{\ϵ}}_r}---\left(6\right)$

Step 4, the decay factor W that will be calculated₁、W₂Respectively with ideal frequency domain E_w、B_wCarry out convolution and obtain frequency domain collapsing field E_G、B_G, carry out the decay electric field E that inverse fourier transform obtains final product time domain_tWith magnetic field B_t；

E_G=E_w×W₁×W₂, B_G=B_w×W₁×W₂ (7)

E_t=ifft (E_G), B_t=ifft (B_G) (8)。